If I understand your question correctly: "Is it OK to quit and restart the "Multi-Play" tourneys?" There is no penalty for quitting a solo, multi-play tournament. You can stop and start as many times as you want.
Play and post your best score. Even if you score your best the first time through, you can continue to play hoping for a better score. When the end of the tournament comes around, only your best score is counted.
I hope that helps.